power transformers are important equipments in power systems. thus there is a large number of researches devoted of power transformers. however, there is still a demand for future investigations, especially in the field of diagnosis of transformer failures. in order to fulfill the demand, the first part reports a study case in which four main types of failures on the active part are investigated based on current diagnostic methods. in details, section 2 presents an overview of power transformers and statistics of transformer failures from a report of cigre. then a test transformer is introduced as an object of the thesis and four failure modes consisting of open-circuit, short-circuit-disc-to-disc, short-circuit-to-ground and ungrounded core are simulated on the test transformer. section 3 introduces the so-called state-of-the-art diagnostic techniques which can be divided into two groups: traditional- and advanced methods. traditional methods such as transformer ratio, magnetic balance, short-circuit impedance tests etc. are performed normally at power frequency. advanced methods such as frequency response analysis, frequency response of stray losses etc. are performed at different frequencies. afterwards, section 4 applies several appropriate traditional- and advanced diagnostic methods to give interpretation for detection of simulated failures on the transformer. furthermore, in order to verify measured results, the finite element method (fem) is exploited for simulation of flux distribution in the transformer in healthy- and open-circuit failure mode.